Answer:
b
Step-by-step explanation:
Calculate the average rate of change between x=-1 and x=1.
Between x=-1 and x=1, the average rate of change is 1.
What is meant by average rate of change?It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:
(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.
Given line in the figure passes through the points A(4, 0), B(-1, -5)
Let the equation of the line be:
y=mx+ c
Slope m=(-5-0)/(-1-4)
m=1
Therefore, y=x+ c
It passes through (4, 0)
y+ c=0
c=-4
y=x-4=f(x)
f(-1)= -1-4=-5
f(1)= 1-4=-3
The average rate of change=(f(b)-f(a))/(b-a)
=(f(1)-f(-1))/1-(-1)
= -3-(-5)/(1+1)
=2/2
=1
Therefore, Between x=-1 and x=1, the average rate of change is 1.
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Modeling multiplication and division fraction pls help
The area of each section is 3/4 square feet. To solve the give question use division operation.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.
Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.
Now convert the mixed fraction with improper fraction:
[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4
[tex]5\frac{1}{4}[/tex] = 21/4
We have to divide the area 7 equal area.
Thus divide 21/4 by 7.
21/4 ÷ 7
To convert the division sign into multiplication sign, take the reciprocal of 7:
21/4 × 1/7
= (21 × 1)/(4 × 7)
Divide the denominator and numerator by 7:
= 3/4
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What integer is tripled when 9 is added to three-fourths of it?
Answer:
4
Step-by-step explanation:
let n be the integer , then n tripled is 3n, so
[tex]\frac{3}{4}[/tex] n + 9 = 3n ( multiply through by 4 to clear the fraction )
3n + 36 = 12n ( subtract 3n from both sides )
36 = 9n ( divide both sides by 9 )
4 = n
the required integer is 4
7. Return on equity will not change if the firm increases its use of debt.
The statement "Return on equity will not change if the firm increases its use of debt" is false.
What is return in equity?Return on equity (ROE) is a financial ratio that shows how well a company is managing the capital that shareholders have invested in it. To calculate ROE, one would divide net income by shareholder equity.
Given is a statement, "Return on equity will not change if the firm increases its use of debt".
As we know that, The equity equals the assets minus total debt, a company decreases its equity by increasing the debt, or we can say, when debt increases, the equity decreases and since equity is ROE's denominator, ROE in turns gets a boost.
Hence, the statement "Return on equity will not change if the firm increases its use of debt" is false.
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During one flu epidemic the proportion of adults nationwide who have come down with the flu is 8%. The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu.
The hypotheses are as follows:
Null hypothesis: proportion of those vaccinated catching the flu = 8%
Alternative hypothesis: proportion of those vaccinated catching the flu < 8%
Select one:
A.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is less than 8%.
B.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is not equal to 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
C.
Rejecting the null hypothesis means there is insufficient evidence that the proportion of those vaccinated catching the flu is equal to 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
D.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
The test hypothesis is
H₀: p=0.08 (null hypothesis) and
Hₐ: p<0.08 (alternative hypothesis )
Given that,
8% of adults in the country contract the flu at any given time during a flu epidemic. The following are the hypotheses:
0% of people who received the vaccine contracted the flu.
8% or less of people who received the vaccine ended up getting the flu.
In order to reject the null hypothesis, there must be proof that 8% of individuals who received the vaccine did not also get the flu.
If the null hypothesis is not rejected, then there is insufficient data to draw the inference that the proportion of people who receive the flu shot is 8%.
The test hypothesis is H₀: p=0.08 (null hypothesis) and Hₐ: p<0.08 (alternative hypothesis )
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TRUE/ FALSE. A researcher compares the BMI of two populations of individuals from different socioeconomic backgrounds and finds that the proportion of individuals considered obese and from a poor background is .37 (n = 112), and the proportion of individuals considered obese and from an affluent background is .27 (n = 87); a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).
True , a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).
The critical value for alpha is 0.05 and z is 1.96 .
The corresponding confidence interval is ( 6.235 , 7.165).
Therefore the above statement is true.
Confidence Interval, to put it simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.
The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.
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the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .
Given :
the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
Quadratic equation :
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
Formula :
= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]
Discriminant = b^2 - 4ac
if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .
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Figure 1 and 2 are shown in the coordinate below.
Saorise claims the there is a sequence of transformations that Carries figure 1 onto figure 2. Select all actions that she could take to justify this claim
A. show that a rotation of 180° counterclockwise about the origin carries Figure 1 onto Figure 2
B. show that a reflection over the x-axis followed by a reflection over the y-axis carries Figure 1 onto Figure 2
C. show that a translation of 4 units right followed by a translation of 5 units down carries Figure 1 onto Figure 2
D. show that a rotation of 90° clockwise about the origin followed by a reflection over the x-axis carries Figure 1 onto Figure 2
Answer:
A and B
Step-by-step explanation:
actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.
Please help asap
Which of the following expressions is equivalent to -6(2x+5)?
(1). -12x-30
(2). -42x
(3). 3-3(4x+11)
(4). -2(6x+15)
A. 1 only
B. 2 and 3
C. 1,3,4
D. 1,2,3,4
Answer:
1st & 4th answers are correct.
Step-by-step explanation:
-6 ( 2x + 5 )
Solve the brackets.
- 12x - 30
We can also write the answer like this.
Take -2 out of the brackets.
- 12x - 30 → -2 ( 6x + 15 )
Therefore, 1st & 4th answers are correct.
Subtract.
−135−(−278)
Enter your answer as a simplified fraction by filling in the boxes.
Answer:143
Step-by-step explanation: When subtracting a negative number from a negative number(a minus sign followed by a negative turns the two signs into a positive sign) you are then adding a positive
Use spherical coordinates to Find the average distance from a point in a ball of radius a to its center.
The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
Given the radius in the question = a
The integration of the total distance before dividing the volume will be =
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]
⇒ [tex]\pi A^{4}[/tex]
Let us divide the average distance by the ball's volume,
⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]
⇒ [tex]{\frac{3a}4}[/tex]
By the use of the Parcly Taxel's way,
Let the radius of the ball be = A
f(x) = probability density function
Distance = D from the given point to the center.
P( D < a )
[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A
Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
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A rally car race course covers 631.95 miles. The winning car completed the course in 7.5 hours. What was the average speed of the winning car?
The average speed of the winning car is 79.38 miles per hour.
Given : Distance covered by rally car race course = 515.97 miles
Time taken to complete the course by winning car = 6.5 hours
The average speed of the winning car = ( Distance covered by rally car race course) ÷ (Time taken to complete the course by winning car)
= (515.97)÷ (6.5) miles per hour
= 79.38 miles per hour
Hence, the average speed of the winning car = 79.38 miles per hour.
What is average speed?Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.Average speed combines two ideas in two words: average, meaning a mean derived from a lot of individual data points, and speed, which is a change in position.You can calculate the average speed for any type of motion if you can time the motion and measure the distance.To learn more about Average speed refer to:
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Solve for X : x + (7 x5) = 25
PLEASE HELP IM GOING TO FAIL
4. What is the graph of the system? (1 point)
y≤x +4
2x+y≤-4
Answer:
A
Step-by-step explanation:
The answer is option A
Hope this helps :)
Using traditional methods, it takes 100 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 260 students and observed that they had a mean of 99 hours. Assume the standard deviation is known to be 6. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places.
The value of the Test statistic =z=-1.67
We have the value of sigma = 6, n = 260
In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.
Now using the formula of Test static
Test statistic will be: [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]
Where, n = total number of sample = 100
[tex]\bar x[/tex] = mean of the given data
[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.
So, putting the value given in the question,
We will get the value of test static as:
[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]
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Amy is going to spend What she saves from her rent budget on entertainment. How much will she’s have for entertainment each month?
Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.
How is the rent budget determined?The total budget for rent, utilities, and food for nine months is given as $12,798.
Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.
This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.
The total budget for rent, utilities, and food for nine months = $12,798
The percentage of the budget for rent = 60%
The amount for rent for nine months = $7,678.80 ($12,798 x 60%)
The monthly rent amount is $853.20 ($7,678.80/9)
Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.
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Question Completion:The percentage of the rent to the total rent, utilities, and food budget is 60%.
The mass of a sample of bacteria has increased by 2% each day for the past 10 days. The initial mass was 5 mg. If this growth continues, which equation can be used to determine M, the mass after d days?
The growth of the mass of the sample of a bacteria is represented by the exponential model m(x) = 5 · 1.02ˣ.
How to predict the growth of the mass of the sample of a bacteria
In this problem we find the case of mass of a sample of a bacteria (m(x)), in miligrams growing in time (x), in days. This growth is done exponentially, the exponential model is shown below:
m(x) = m' · (1 + r / 100)ˣ
Where:
m' - Initial mass, in miligrams.r - Growth rate, in percentage.x - Time, in days.We have that the mass of the sample was initially 5 miligrams and grows at a rate of 2 % during 10 days. If we know that m' = 5 mg and r = 2, then the exponential model for the sample is:
m(x) = 5 · 1.02ˣ
The exponential model for the sample of a bacteria is equal to m(x) = 5 · 1.02ˣ.
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the value of y varies directly with x.when y=75 x=1/2 what is the value of y when x equals 2 1/4
The value of y from the equation y = 150x when x = 2(1/4) is 337.5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
y varies directly with x.
y ∝ x
y = kx
Now,
y = 75 when x = 1/2
75 = k(1/2)
k = 75 x 2
k = 150
Now,
y = kx
y = 150x
When x = 2(1/4) = 9/4
y = 150 x 9/4
y = 337.5
Thus,
The value of y is 337.5.
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Question 2 of 10 A tessellation could be created using circles like the one shown below. A. True B. False
Answer:
B. False
Step-by-step explanation:
You want to know if it is true that a tessellation can be created from circles.
TessellationA tessellation is the covering of a plane, using one or more geometric shapes with no overlaps and no gaps.
As the attachment shows, it is not possible to cover a plane with circles, leaving no gaps.
A tessellation cannot be created using circles. The proposition is False.
please help its holding back my grade 50 points
Answer:
X=54
Step-by-step explanation:
equate both the equations since angles of opposite sides are equal
2x+2=3x-52
3x-2x= 52+2
x=54
answer:
x=54
Step-by-step explanation:
2x+2=3x-52
move the 2x to 3x because x can't be negative
and add 52 to 2 so x=54
Translate this phrase into an algebraic expression.
19 increased by twice a number
Use the variable n to represent the unknown number.
The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
What is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.
To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:
Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).
Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.
Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:
19 + 2n
Hence, the expression represents the result of adding 19 to twice a number is 19 + 2n.
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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
What is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.
To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:
Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).
Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.
Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:
19 + 2n
Hence, the algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
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Factor x^3-125 as shown in the image attached
Answer:
Factored form is (x - 5) (x² + 5x + 25)
Step-by-step explanation:
You can get the factors directly by using the formula for a³ - b³.
Liana consumes only beer and chips. Her indifference curves are all bowed inward. Consider the bundles (2,6), (4,4), and (6,2). If Liana is indifferent between (2,6) and (6,2), then Liana must
prefer (4,4) to (6,2).
If Liana is indifferent between the bundles (2,6) and (6,2), then it means that she values these two bundles equally. This means that Liana does not have a preference for one bundle over the other.
If Liana's indifference curves are bowed inward, it means that she is willing to give up more units of one good in order to get more units of the other good, as she moves along the indifference curve. This implies that Liana has a diminishing marginal rate of substitution (MRS) between the two goods.
Therefore, if Liana is indifferent between (2,6) and (6,2), it does not necessarily follow that she prefers (4,4) to (6,2). It is possible that Liana may also be indifferent between (4,4) and (6,2), or she may prefer (6,2) to (4,4). This would depend on the specific shape and location of Liana's indifference curves.
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Need help fast thank you
landon's ice cream machine produced 1.2 cups of ice cream in 3 minutes. If it produced the same amount each minute, how much ice cream did the machine produce during the 2nd minute?
The ice cream that the machine produces during the 2nd minute will be 0.8 cups of ice cream.
How to illustrate the rate?Rate demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator. By condensing them into the simplest form possible, we can calculate the rate.
A rate is a ratio that contrasts two distinct quantities represented by various units. A comparison of two numbers with various quantities or units is called a rate. A ratio or a rate out of 100 is what is known as a percentage.
Here, landon's ice cream machine produced 1.2 cups of ice cream in 3 minutes. If it produced the same amount each minute, the ice cream that the machine produces during the 2nd minute will be:
= (1.2 / 3) × 2
= 0.4 × 2
= 0.8 cups.
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The manager of a food company wants to conduct a survey to find out whether consumers like or dislike a new brand of soup that was recently launched. Which of the following data collection methods is mostly likely to get unbiased results? a. Ask distributors who supply the products to local retailers about the popularity of different soup brands. b. Ask the employees in the company which soup is the best. c. Ask customers who visit retailers within a 15 mile radius of the company headquarters. d. Ask customers who visit the grocery store nearest to the manager's house which soup they like the best.
Option c is most likely to get unbiased results.
The best option for collecting unbiased data in this case would be option c: asking customers who visit retailers within a 15 mile radius of the company headquarters. This method would involve sampling a diverse group of customers who are not affiliated with the company in any way, and therefore are likely to provide more objective feedback about the new brand of soup.
Option a, asking distributors who supply the products to local retailers about the popularity of different soup brands, could be biased because the distributors may have their own interests in promoting certain brands over others.
Option b, asking the employees in the company which soup is the best, could also be biased because the employees may have a vested interest in the success of the company and its products, and therefore may not provide completely objective feedback.
Option d, asking customers who visit the grocery store nearest to the manager's house which soup they like the best, could also be biased because it may not be representative of the overall customer base for the soup. It is important to sample a diverse group of customers in order to get a more accurate sense of how the new brand of soup is being received.
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You are making snack bags to sell at the fair. You want each bag to contain the same combination of carrot and celery sticks. You have 75 carrot sticks and 40 celery sticks and want to use them all.
What is the greatest number of snack bags you can make
The greatest number of snack bags is 10.
Highest Common Factor:The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).
HCF is a fundamental method that allows you to equally distribute items throughout a group or set.
We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.
Here we have
Number of carrots = 75
Number of celery sticks = 40
Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.
To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below
Write given numbers as the product of prime numbers
=> 70 = 2 × 5 × 7
=> 40 = 2 × 2 × 2 × 5
List out the common factors
=> 2 × 5
=> HCF (70, 40) = 10
Therefore,
The greatest number of snack bags is 10.
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19 points all i have really..Gavin is hoping to buy his first car in 3 years. He is considering two options to help him save and grow his money. If he currently has $800, should he deposit his money into a savings account that is compounded annually at an interest rate of 9% or in a savings account that is compounded quarterly at an interest rate of 3%?
Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
Given that the current balance is $800.
There were two types of schemes.
First scheme offer compounded annually at an interest rate of 9%
Second scheme offer compounded quarterly at an interest rate of 9%.
The formula of compound interest annually is
A = P(1+r)^t
P = principal = 800
r = rate of interest = 9% = 0.09
t = time = 3 year
A = 800(1+0.09)³
A = 1036.02.
The formula of compound interest annually is
A = P(1+(r/n))^tn
P = principal = 800
r = rate of interest = 3% = 0.03
t = time = 3 year
n = 4
nt = 4×3 =12
A = 800(1+0.03/4)¹²
A = 875.04
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I need help with my math homework
The multiplications, applying the associative property, are given as follows:
1. (5 x 2) x 3 = 10 x 3 = 30.
2. 4 x (3 x 3) = 4 x 9 = 36.
3. (6 x 1) x 4 = 6 x 4 = 24.
4. 5 x (2 x 4) = 5 x 8 = 40.
5. (2 x 2) x 8 = 4 x 8 = 32.
6. 3 x (2 x 2) = 3 x 4 = 12.
7. (4 x 2) x 4 = 8 x 4 = 32.
8. 6 x (3 x 3) = 6 x 9 = 54.
What is the associative property of multiplication?The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.
In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.
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if a crew of six workers completes a job in 15 hours how long will it take 10 workers to complete the same job
As no. of crews and time are inversely proportional 10 workers will finish the job in 10 hours.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, A crew of six workers completes a job in 15 hours.
We know more crew will finish the job in less no. of hours so they are inversely proportional.
So, C = k/t.
6 = k/15.
k = 90.
Now, C = 10 hence,
10 = 90/t.
t = 90/10.
t = 10 hours.
So, They can finish in 10 hours.
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